Solvability of a boundary value problem at resonance

A Guezane-Lakoud; R Khaldi; A Kılıçman

doi:10.1186/s40064-016-3172-7

Solvability of a boundary value problem at resonance

Springerplus. 2016 Sep 7;5(1):1504. doi: 10.1186/s40064-016-3172-7. eCollection 2016.

Authors

A Guezane-Lakoud¹, R Khaldi¹, A Kılıçman²

Affiliations

¹ Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria.
² Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor Malaysia.

Abstract

This paper concerns the solvability of a nonlinear fractional boundary value problem at resonance. By using fixed point theorems we prove that the perturbed problem has a solution, then by some ideas from analysis we show that the original problem is solvable. An example is given to illustrate the obatined results.

Keywords: Banach contraction principal; Existence of solution; Fractional boundary value problem at resonance; Schaefer fixed point theorem.